Programming Mathematica to find normal mode frequencies for a system with a large number of degrees of freedom

Imagine a system of N masses alternating with N+1 springs in a line between two walls, with all motion constrained to the line. This system has N normal modes, each with its own frequency. Using only basic knowledge of programming principles, we developed a program in Mathematica that allowed us to generate the frequencies of these normal modes for any value of N, including large N. In this talk we present the specific strategy, structure, and products of the program. In particular, we defined a function for filling matrices and used nested loops to extract relevant data. In a companion talk, we present physical arguments for patterns we observed in the sets of frequencies.